It makes the process a lot easier, but you don't have to. Just find the common denominator and multiply, divide, add, or subtract. Using graphs or charts such as the pie chart also helps understand the basic concept of it. Such as 1 3/5 + 1 2/3. A calculator does make this handy if you have one. Just turn it into an improper fraction and add. This process simplifies the complications of this branch of math a lot.

First understand that x/y means "x" parts of a "whole" which is divided into "y" parts.. Now an example: Suppose a class has 100 students, for a particular task 1/4 students were selected, and other 1/5 students were selected for a 2nd task. Find how many students have been selected from the class in all. [(1/4 + 1/5) * 100] = ?Solution,1/4 of the class will be 1/4 * 100 = 25 ; 1/5 of the class will be 1/5 * 100 = 2025+20 = 45; the answer will be 45 studentsBut if we directly add both the fractions we get 1/4 + 1/5 = 2/9 ; 2/9 * 100 = 22.22 students; which is not the correct answer.To solve this problem we need to first find a LCM (Lowest Common Multiple) of the denominators (4 & 5) which is 20.Now 1/ 4 becomes 5/20 and 1/5 becomes 4/20; So 1/4 + 1/5 is now = 5/20 + 4/20 = 9/20 9/20 * 100 = "45" the correct number of students. Thus finding LCM means finding a common number of parts; which also keep the ratio same; 1/4 = 5/ 20 and 1/5 = 4/20. Hope this helps..

It's a similar reason to why you need common units to combine measurements. If I had three cups plus two pints, I couldn't add it together and get five cup+pints. That doesn't even make sense, because "cup+pint" is not a unit of measure.

I would first have to convert them both to cups and get three cups plus 4 cups = 7 cups. (Or I could convert them both to pints and get 1.5 pints + 2 pints = 3.5 pints.)

You can think of the denominator of a fraction as being similar to a unit of measure.

Because if not, then you won't be able to add or subtract properly and you will get a completely different answer. but if you multiply or divide fraction, you won't need the same denominators. just for adding and subtracting. Hope this Helps!! :)

If the denominators are not the same, then your answer will come out wrong. For example, say you had 5/6 and 3/4. If you just added them with different denominators, it would come out as 8/10. (4/5), but instead it would be 10/12+9/12=19/12, or 1 7/12.

In some cases denominators are equal to make some of the questions easier, likeExample: A person bought 8/10 kgs of sugar and another person bought 2/10 of it. So how much is left in the bagAnswer: Nothing

because say you want to add the 2 numbers the nmbers need to be the same in order to add them witch them means that the numbers need to be the same in order to add them but with subtracting you need to find common numbers that still work in order for you to do the subtracting but if you are multiplying the numbers you still need to find denomiters that will work for both. And for dividing then you need to still need find common denimatiors so then you need to dived the numbers the by the top then the bottom

If the domeator is in the same you can't add it so you need to find what 3 and the 7 have the same multiplies that means you have to multiply 3 times 7 do with the numerator then 7 times 3 then add with numerator then add the numerators and if it is greater then domerator then divided the numerators altogether then tat is you're answer.

Good question.In mathematics, the concept of adding and subtracting fractions require the denominator to be common. The numerator does not need to be common but the denominator must be.If the denominator wasn't common how would we work out the question?E.g. 1/3 + 3/7 = ?To work out this question, we would have to find the LCM (Lowest Common Multiple) of the denominators; in this case, 3 and 7. Then when we find that it is 21 we can adjust the numerators to 7 and 9. With that done, we can add 3 and 7 to make 10 over the denominator, which is 21.

This is why the denominators have to be common. There was no equation or formula built in the concept of adding and subtracting fractions that do not require the denominators to be common.

It's much better to have them the same denominator because it's way less complex (which means easier). I don't know if there is a way you can add up fractions with unlike denominators but if there is without all the abracadabra, then I'll let you guys know :) But, like I said, it's way less complex if their the same denominator :D Hope this helped. By the way, that's just the way somebody invented fractions -_-

why? Okay.You can add 3/8+5/8=8/8fairly easily because the denominators are the same.However, if you did not change the denominators then this is what it would be like:2/8+3/5=?You cant do it because the denominators are not equal. You can't add 2+3=5and 8+5=13 and get 5/13. They aren't equal fractions and you don't add denominators.

It would be like going to the store and saying I want 2/grapes plus 2/apples. They cant bring you out 4/apples or 4/grapes and say that they have satisfied your order. Same thing with fractions with differing denominators. Nor could they say that grape flavored/apples is the same thing as an apple flavored/grapes. They have totally different tastes and sizes depending on what is on the top/bottom ;)

Imagine we'v got 2 identical apples: apple A and apple B (The denominator is the total number of pieces in each case and the numerator is the number of pieces out of the whole we are working with in each case) : 1.We cut apple A into 2 pieces of the same size and we cut apple B into 8 pieces of the same size.2. You will agree with me that the one piece of apple A will be larger in size than one piece of apple B. 3. If we represent one piece of apple A in terms of fraction, we'll get 1/2. (Meaning 1 piece of apple out of the 2 pieces. The denominator represents the total no. of pieces) If we represent one piece of apple B in terms of fraction, we'll get 1/8. (Same logic. Remember we cut apple B in 8 pieces)4. Since one piece of apple A is not of the same size as one piece of apple B, we cannot add them and get a number directly. We cannot say 1/2 + 1/8= 2/10. (meaning we cannot say that a piece of an apple divided by 2 and another of an apple divided by 8 when added will give us 2 identical pieces out of 10 identical ones. Remember the denominator represents the number of pieces)5. To get a number, we need to get the pieces of apple A of the same size as those of apple B. For that, we'll need to reduce apple A to 8 pieces too. Only then can we get identical pieces everywhere and thus add effectively.6. To reduce apiece of apple A to the same size as one of apple B, we need to divide 1/2 by 1/8. This will give us 4. Each of the 2 pieces of apples in apple A will be cut into 4, thus getting 8 identical pieces. One piece of apple A will therefore represent one eighth of the whole apple.7. With both apple A and apple B being divided into 8 pieces of the same size, calculations can be effectively carried out. We can easily add 1 piece of apple A with one piece of apple B. We can say 1/8 (of apple A) + 1/8 (of apple B)= 2/8 (meaning 2 identical pieces of apples out of 8 identical ones)

Or you can think of it in an easy way. Let's say the denominators are very special. Each one is unique. Let's say the denominator 4 is an orange, and the denominator 8 is an apple. You can't add apples and oranges because their values are different in the market. 4 oranges may be $5, but 4 apples could be $6.50.

Good help- now to make another math problem- adding multiple fractions eg)1/2 + 3/5 + 4/7= Actually Mom knows the method- but the 15 year old can't figure out w/ a lot of examples from a good book. However KHAN makes an excellent teaching explanation!!!

ok when he says to simplify he means that u need to make the fraction into its lowest terms lets say u have 10/20 it becomes 5/10 then it becomes 1/2 it just means to make it small like break it up and to do so u need to make a factor rainbow i believe

It works like this. And I'll use a fraction OTHER than 1/2.If you have a fraction like 40/120 in a problem on Khan Academy, it won't accept it as an answer. It has to be in simplest form, simply because it's easier to grade for teachers, the website, and you. It simplifies to 1/3 because you can break it down.

When you simplify you have to make the fraction into the lowest possible fraction. If you have 4/12 you can simplify it. You can divide them both by two. So that would make the fraction now 2/6. You can simplify it lower by dividing it by two again to 1/3. If the fraction is 5/8 you can't divide it any lower because 5 is a prime number. A prime number can only be 1 and itself. Like five. You can't divide it any lower.

It means to make the problem simpler.Or fraction simpler.For example if you have 6/8,6 out of 8 simplifies to 3/4.Because 6=2*38=2*4The 2s cancel out to be just 1.So there is just 3/4 left.Hope this helps:)

You have to find the greatest common factor of the numerator and the denominator of the fraction you are simplifying (GCF). Like in the example 4/8 = 1/2, I listed the factors of four and eight. Four: 1,2,4 and eight: 1,2,4,8. Then I listed the common factors. Those are the factors that both numbers have. In this case, 1,2, and 4. Then I select the largest one(4), so as to make the fraction in simplest form. Then I divide both the numerator and the denominator of the original fraction; 4/4=1, 8/4=2. And there you have the fraction in simplest form; 4/8=1/2.For more info see http://www.mathisfun.com/simplifying-fractions.htmlHope this helped, Tesla

You divide the numerator and the denominator by the same number. If the numerator or the denominator don't share any common factors, you're done. If not, divide them both by another (or the same) number until you run out of factors. Just remember that both of the numbers have to stay as whole numbers.

1/2+3/4=? lets try that. well the denominator needs to be the same so we have to find a common mutiple of 2 and 4. they both go into 4. so, 1/2 becomes 1/4. but, since 2x2=4,we have to mutiply 1 by to also. so, we end up with 2/4. 3/4 stays the same because we are using 4 as the denominator. 4x1=4, and 3x1=3. so, we end up with 2/4+3/4=? well, you only add the numorators, so that would be 5/4. but, the numorator is larger than the denominator. so, you look at the denominator,which is 4, and subtract the numorator,which is 5. so, the final answer is 1 1/4. hope this helps. if not, please comment me about it.

The denominators "denote" what the fraction is counting by (who many is in a whole). This is how we know what portion of a group is selected. For example: I have 10 marbles and 5 of them are blue. What fraction of marbles are blue? 5/10. The denominator being the total number in the group and the numerator being how many. Now if I were asking to add the number of blue marbles to the number of marbles that you don't know the color of, you would say 5/10 + 5/10 = 10/10 or 1. This being true we can see that we are adding numerators of the same grouping. IF this were not true, i.e. adding numerators without like denominators we would get an answer that didn't make sense. ex. 1/10 + 2/100= ? if you said 3/100. Let's think of money with this example. It would be the same as saying 1 dime plus 2 pennies equals 3 pennies and we know that's incorrect. Therefore, we have to trade the dimes in for pennies giving us 10/100 + 2/100= 12/100. Which makes sense because we know that 1 dime can trade in for 10 pennies and 10 pennies + 2 pennies would equal 12 pennies. I hope this helps.

a fraction with the same denominator makes adding or subtracting the fraction A LOT easier!!It also takes less time to figure out the answer while on the other had different denominators can take time to answer cuz in different denominators u usually have to find the LCD

Imagine we'v got 2 identical apples: apple A and apple B (The denominator is the total number of pieces in each case and the numerator is the number of pieces out of the whole we are working with in each case) : 1.We cut apple A into 2 pieces of the same size and we cut apple B into 8 pieces of the same size.2. You will agree with me that the one piece of apple A will be larger in size than one piece of apple B. 3. If we represent one piece of apple A in terms of fraction, we'll get 1/2. (Meaning 1 piece of apple out of the 2 pieces. The denominator represents the total no. of pieces)If we represent one piece of apple B in terms of fraction, we'll get 1/8. (Same logic. Remember we cut apple B in 8 pieces)4. Since one piece of apple A is not of the same size as one piece of apple B, we cannot add them and get a number directly. We cannot say 1/2 + 1/8= 2/10. (meaning we cannot say that a piece of an apple divided by 2 and another of an apple divided by 8 when added will give us 2 identical pieces out of 10 identical ones. Remember the denominator represents the number of pieces)5. To get a number, we need to get the pieces of apple A of the same size as those of apple B. For that, we'll need to reduce apple A to 8 pieces too. Only then can we get identical pieces everywhere and thus add effectively.6. To reduce apiece of apple A to the same size as one of apple B, we need to divide 1/2 by 1/8. This will give us 4. Each of the 2 pieces of apples in apple A will be cut into 4, thus getting 8 identical pieces. One piece of apple A will therefore represent one eighth of the whole apple.7. With both apple A and apple B being divided into 8 pieces of the same size, calculations can be effectively carried out. We can easily add 1 piece of apple A with one piece of apple B. We can say 1/8 (of apple A) + 1/8 (of apple B)= 2/8 (meaning 2 identical pieces of apples out of 8 identical ones)

Because when you add or subtract you only add or subtract the numerator, and not the denominator. If you have a different denominator for each fraction, say you had 3/4 + 18,you can, not, add the denominator AND numerator, because if you do, you get 6/12, which is the wrong answer and if that was the way we added fractions it would be way too easy. So you need to find the common denominator, by listing the two denominators for each fraction:4:8:then writing out the multiples,4: 4, 8,8: 8,then once you find a common multiple, that common multiple becomes the denominator:3/8 + 1/8And since you changed the denominator for one of the fractions, you change the numerator for that fraction, according to the difference for what that fraction's denominator used to be, to what it now is:3/4 -> 3/8 4 x 2= 8So then you do that change to the numerator to even it out:In 3/4, the numerator is= 3So you do 3 x 2, which equals 6, so your new fraction and numerator is 6/8.

Now you have 6/8+1/8, and since you ONLY add the numerator, you get 7/8 for your answer.

Why did he say to turn the nine in to a 36 and why multiply by 4 what.]nine times four is thirty six but why cant the nine just be nine. I'm confused ):and why do we have to multiply the numerator by 4 too.~_~

to add fractions, you need to have the denominator the same. these two fractions have denominators of 9 and 12. The lowest common multiple of these two numbers is 36. That requires multiplying by x4 and x3 respectively. We multiply the numerator and denominator by the same number so the number does not change. 4/9 * 4/4 = 16/36. 4/4 is the same as 1, so the number doesn't change

at first i felt like you so i know what you mean. If you are multiplying with unlike denominators then you need to multiply the denominators by each other so that they are the same. Then you have to multiply the numerator by the other denominator as to make the number not change. If you didn't , it would be a totally different fraction!

the reason why is because in order for the fractions to add ,the denominator has to be the same as the other and so that is why the numerator has to change because the denominator is increasing and so it only makes sense that the numerator increase to

No. If the denominators are unlike you are comparing two completely different things. Think of fractions like pizza. The total number of slices is the denominator. What happens when you increase the total number of slices while keeping the pizza the same size? The slices get smaller. A pizza with 4 slices will have smaller slices than a pizza with just 3 slices. So if you don't keep the denominator (or number of slices) the same your definition of what constitutes a slice (or fraction) changes and your answer no longer makes sense. It maybe easier to comprehend if you see it visualized, checkout http://mathmistakes.info/facts/AlgebraFacts/learn/fr/add.html

You have to do the same thing, for instance, take 1/3 - 4/5.First, list the multiples.3= 3, 6, 9, 12, 15, 18, 21, 245= 5, 10, 15, 20, 25, 30, 35The least common multiple is 15. So the problem would become ?/15 - ?/15. Since 3 times 5= 15, you have to multiply 1 by 5, which = 5. The problem becomes 5/15 - ?/15. Since we also multiplied 5 times 3= 15, we have to do that to 4. 4 times 3= 12.The problem becomes 5/15 - 12/15.Because the answer is going to come out negative, here is a trick.Subtract 12 - 5. (answer is 7)Stick a negative sign in (-7) and your answer is - 7/15.Hope I Helped! ;D

Hi there, I will show an example because this is better than explaining. If I explained it to you would be lost. So an easier way is easier to understand.

Mr. McFattenMeUp has 4/8 of a chocolate cake in his refrigerator. Later his friend Mr. MeFillMyTummy gave him 3/4 of a vanilla cake. How many cakes does Mr. McFattenMeUp has all together?

(0)(0)(0)(0)( )( )( )( ) 4/8( 0 )( 0 )( 0 )( ) 3/4

I got this diagram ready. now if I were to add them both without converting them you would get 7/12 and the answer would look like this

[|][|][|][|][|][|][|]00000 7/12

And this would be false since if you combine my previous diagram you would get this

[(0)(0)(0)(0)( 0 )( 0 )] ( 0 ) 1 and 1/4

The reason why we change the denominator is because the pieces of chocolate and vanilla cake have different size. So to get the correct answer, we change the denominator to make the pieces of chocolate and vanilla cake have same size. I showed you the answer but lets do the math anyways.

(0)(0)(0)(0)( )( )( )( ) + ( 0 )( 0 )( 0 )( )4/8 3/4

( 0 )( 0 )( 0 )( ) --> (0)(0)(0)(0)(0)(0)( )( )

3/4 times 2 on both sides is 6/8 and 2 x 4 is 8 so the slice changes from ( 0 ) to (0)So...

(0)(0)(0)(0)( )( )( )( ) + (0)(0)(0)(0)(0)(0)( )( )4/8 6/8

And we add them up which we get:

[(0)(0)(0)(0)(0)(0)(0)(0)] (0)(0) 10/8 which is 1 2/8

Now we must simplify them.

2/8 --factor--> (2)/(2 x 2 x 2)

We can cross off one 2 since it exists in both numerator and denominators and we get.(2)/(2 x 2 x 2) --> 1/(2 x 2) --> 1 and 1/4 (I took out 1 temporary because adding it to the fraction while I was simplifying might have confused you)

So Mr. McFattenMeup has 1 and 1/4 of cakes altogether

Hope this helped and your curiosity has rewarded you with a +1 vote :D

Hi there, no you do not have to divide the number because 1 and 13/36 cannot be divided any further. However if the answer was 1 and 12/36, it would be divisible.

12/36 (2 x 2 x 3)/(2 x 2 x 3 x 3)I factored themNow I cross off the numbers that exist in both numerator and the denominator.(2 x 2 x 3)/(2 x 2 x 3 x 3) --> 1/3 since there are 2 of 2 and 1 of 3 that exist in both sides. I placed 1 in the numerator on the top because all of the number in there has been crossed off. So the answer is 1 and 1/3

But in the problem that Sal gave us, 1 and 13/36 cannot be divisible any further.

it is quite simple if you ask me all you have do is this Whenever you add fractions with unlike denominators, you must make the denominators of the same value. In this example, the easiest approach is to multiply 8 x 3 to get 24. Here, you multiply by 3 to get . Then you multiply the second equation by 8 to get . Note that both addends have 24 as a denominator. Add in the same manner as with the unit Adding fractions with like denominators.

For adding fractions with unlike denominators, you would need to change the numbers below the bar (denominators) by finding the least common factor/multiple.Example:3/4 + 3/16Convert 3/4 to sixteenths.4 (4) is 163 (4) is 12Both numerators have to be multiplied by the same numbers.12/16 + 3/16 = 15/16Hope this helps!

Don't worry I learned this in class. The way I do it is stacking the two fractions then putting equal signs and fraction bars. Multiply the two denominators and that is your Least Common Factor. Then you add the numerators and then BOOM! Awnser is there. Only simplify if directed in math book. JUST evaluate if simplifying not needed.

Excellent question my friend. If you had two fractions like 6/5 and 7/5 you would get 13/5. That is what you would call a improper fraction. In arithmetic you wouldn't leave it like that because it's considered a improper fraction. You would need to change it into a mixed number. When you get to algebra 1 they will allow you to leave it as a improper fraction as an answer to a problem.

It doesn't have to but if you are in 5th grade, you haven't learned about that yet. If it is smaller, it is a proper fraction. If the numerator is larger than the denominator, that just means it is an improper fraction and it hasn't yet been reduced into whole numbers.

In order to add fractions, the denominators must be the same.The lowest common denominator or multiple (LCD or LCM) is 4.Whatever we multiply the denominator by, we must multiply the numerator by.Therefore, 1/2 = 2/4.So, 3/4 + 2/4 = 5/4 as an improper fraction or as 1 1/4 as a mixed number.

Good question. The answer is that if you didn't then you would change the value of the fraction. Like 2/3. If you multiplied both of them by 2, you would have 4/6. Both equal 0.66. If you multiplied the bottom only, then it would be 2/6 which is equal to 0.33. It would change the value.

If you're adding a fraction, you must have denominators that are alike. For example, if you are adding 1/4 + 1/3, you have to make both the denominators the same. So the lowest common denominator for 4 and 3 is 12, so you would multiply 1/4 by 3 and get 3/12. Then you would multiply 1/3 by 4 because you need to get the denominator to 12, and 3 times 4 is 12. So you would get 4/12. Now you would add 3/12 and 4/12 together and get 7/12. I hope this helped and good luck!

It's because the two fractions aren't connected. You can multiply one by three and the other by four and they wouldn't affect each other. As long as the numerators are also being multiplied, you can keep multiplying and switching and dividing forever. I don't usually do this because it only works with a few fractions, and then there's the decimals to worry about, but it can be fun.